Accurate direct numerical simulations are performed to determine the drag, lift and torque coefficients of non-spherical particles. The numerical simulations are performed using the lattice Boltzmann method with multi-relaxation time. The motivation for this work is the need for accurate drag, lift and torque correlations for high Re regimes, which are encountered in Euler-Lagrangian simulations of fluidization and pneumatic conveying of larger non-spherical particles. The simulations are performed in the Reynolds number range 0.1 ≤ Re ≤ 2000 for different incident angles φ. Different tests are performed to analyse the influence of grid resolution and confinement effects for different Re. The measured drag, lift and torque coefficients are utilized to derive accurate correlations for specific non-spherical particle shapes, which can be used in unresolved simulations. The functional forms for the correlations are chosen to agree with the expected physics at Stokes flow as well as the observed leveling off of the drag coefficient at high Re flows. Therefore the fits can be extended to regimes outside the Re regimes simulated. We observe sine-squared scaling of the drag coefficient for the particles tested even at Re = 2000 withFurthermore, we also observe that the lift coefficient approximately scales as C L,φ = (C D,φ=90 • − C D,φ=0 • ) sin φ cos φ for the elongated particles. The current work would greatly improve the accuracy of Euler-Lagrangian simulations of larger non-spherical particles considering the existing literature is mainly limited to steady flow regimes and lower Re.

The flow around different prolate (needle-like) and oblate (disc-like) spheroids is studied using a multi-relaxation-time lattice Boltzmann method. We compute the mean drag coefficient C D,φ at different incident angles φ for a wide range of Reynolds numbers (Re). We show that the sine-squared drag law2 φ holds up to large Reynolds numbers Re = 2000. Further, we explore the physical origin behind the sine-squared law, and reveal that surprisingly, this does not occur due to linearity of flow fields. Instead, it occurs due to an interesting pattern of pressure distribution contributing to the drag at higher Re for different incident angles. The present results demonstrate that it is possible to perform just two simulations at φ = 0• and φ = 90• for a given Re and obtain particle shape specific C D at arbitrary incident angles. However, the model has limited applicability to flatter oblate spheroids, which do not exhibit the sine-squared interpolation, even for Re = 100, due to stronger wakeinduced drag. Regarding lift coefficients, we find that the equivalent theoretical equation can provide a decent approximation, even at high Re, for prolate spheroids.

This work provides a recipe for creating drag, lift and torque closures for static assemblies of axisymmetric, non-spherical particles. Apart from Reynolds number Re and solids volume fraction ǫ s , we propose four additional parameters to characterize the flow through non-spherical particle assemblies. Two parameters consider the mutual orientations of particles (the orientation tensor eigenvalues S 1 and S 2 ) and two angles represent the flow direction (polar and azimuthal angles α and β). Interestingly, we observe that the hydrodynamic forces on the particles are independent of the mutual particle orientations. Rather, the most important parameter representing the particle configuration itself is the incident angle φ of the individual particles with respect to the incoming flow. Moreover, we observe that our earlier finding of sine-squared scaling of drag for isolated particles (Sanjeevi & Padding 2017) holds on average even for a multiparticle system in both the viscous and inertial regimes. Similarly, we observe that the average lift for a multiparticle system follows sine-cosine scaling, as is observed for isolated particles. Such findings are very helpful since the pressure drop of a packed bed or porous media can be computed just with the knowledge of orientation distribution of particles and their drag at φ = 0 • and φ = 90 • for a given Re and ǫ s . With the identified dependent parameters, we propose drag, lift and torque closures for multiparticle systems.

Various curved no-slip boundary conditions available in literature improve the accuracy of lattice Boltzmann simulations compared to the traditional staircase approximation of curved geometries. Usually, the required unknown distribution functions emerging from the solid nodes are computed based on the known distribution functions using interpolation or extrapolation schemes. On using such curved boundary schemes, there will be mass loss or gain at each time step during the simulations, especially apparent at high Reynolds numbers, which is called mass leakage. Such an issue becomes severe in periodic flows, where the mass leakage accumulation would affect the computed flow fields over time. In this paper, we examine mass leakage of the most well-known curved boundary treatments for high-Reynolds-number flows. Apart from the existing schemes, we also test different forced mass conservation schemes and a constant density scheme. The capability of each scheme is investigated and, finally, recommendations for choosing a proper boundary condition scheme are given for stable and accurate simulations.

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